// 中考专题 - 初中数学综合题型（50题）
export const 中考专题_QUESTIONS = [
  {
    stem: '已知x² - 5x + 6 = 0，求x的值。',
    difficulty: 2,
    answer: [2, 3],
    hint1: '因式分解',
    hint2: '(x-2)(x-3) = 0',
    solution: '【解题】\\nx² - 5x + 6 = 0\\n(x-2)(x-3) = 0\\nx = 2或x = 3\\n\\n答：x = 2或3。'
  },

  {
    stem: '化简：(a+b)² - (a-b)²',
    difficulty: 2,
    answer: ['4ab'],
    hint1: '平方差公式',
    hint2: '[(a+b)+(a-b)][(a+b)-(a-b)]',
    solution: '【解题】\\n(a+b)² - (a-b)²\\n= [(a+b)+(a-b)][(a+b)-(a-b)]\\n= 2a×2b\\n= 4ab\\n\\n答：4ab。'
  },

  {
    stem: '解方程组：{x+y=5, 2x-y=1}',
    difficulty: 2,
    answer: [2, 3],
    hint1: '加减消元法',
    hint2: '两式相加',
    solution: '【解题】\\nx + y = 5 ①\\n2x - y = 1 ②\\n\\n①+②：3x = 6\\nx = 2\\n\\n代入①：2 + y = 5\\ny = 3\\n\\n答：x = 2，y = 3。'
  },

  {
    stem: '已知函数y = 2x + 1，当x = 3时，求y的值。',
    difficulty: 1,
    answer: [7],
    hint1: '代入x = 3',
    hint2: 'y = 2×3 + 1',
    solution: '【解题】\\ny = 2x + 1\\n当x = 3时：\\ny = 2×3 + 1 = 7\\n\\n答：y = 7。'
  },

  {
    stem: '在Rt△ABC中，∠C = 90°，AC = 3，BC = 4，求sin A的值。',
    difficulty: 2,
    answer: [0.8],
    hint1: 'sin A = BC/AB',
    hint2: 'AB = 5',
    solution: '【解题】\\nAB = √(3² + 4²) = 5\\n\\nsin A = BC/AB = 4/5 = 0.8\\n\\n答：sin A = 0.8。'
  },

  {
    stem: '已知一元二次方程x² + px + q = 0的两根为2和3，求p和q的值。',
    difficulty: 3,
    answer: [-5, 6],
    hint1: '韦达定理',
    hint2: 'x₁+x₂ = -p，x₁x₂ = q',
    solution: '【解题】\\n由韦达定理：\\nx₁ + x₂ = -p\\n2 + 3 = -p\\np = -5\\n\\nx₁x₂ = q\\n2×3 = q\\nq = 6\\n\\n答：p = -5，q = 6。'
  },

  {
    stem: '化简：√12 + √27 - √48',
    difficulty: 2,
    answer: ['√3'],
    hint1: '√12 = 2√3',
    hint2: '√27 = 3√3，√48 = 4√3',
    solution: '【解题】\\n√12 + √27 - √48\\n= 2√3 + 3√3 - 4√3\\n= √3\\n\\n答：√3。'
  },

  {
    stem: '解不等式：3x - 5 > 2x + 1',
    difficulty: 1,
    answer: ['x > 6'],
    hint1: '移项',
    hint2: '3x - 2x > 1 + 5',
    solution: '【解题】\\n3x - 5 > 2x + 1\\n3x - 2x > 1 + 5\\nx > 6\\n\\n答：x > 6。'
  },

  {
    stem: '已知二次函数y = x² - 4x + 3，求顶点坐标。',
    difficulty: 2,
    answer: ['(2,-1)'],
    hint1: '配方法',
    hint2: 'y = (x-2)² - 1',
    solution: '【解题】\\ny = x² - 4x + 3\\n= (x² - 4x + 4) - 1\\n= (x-2)² - 1\\n\\n顶点坐标为(2, -1)\\n\\n答：顶点(2, -1)。'
  },

  {
    stem: '在△ABC中，AB = AC，∠A = 40°，求∠B的度数。',
    difficulty: 1,
    answer: [70],
    hint1: '等腰三角形',
    hint2: '∠B = ∠C = (180°-40°)/2',
    solution: '【解题】\\n∵ AB = AC\\n∴ ∠B = ∠C\\n\\n∠B + ∠C = 180° - 40° = 140°\\n∠B = 70°\\n\\n答：∠B = 70°。'
  },

  {
    stem: '计算：(-2)³ + 2² - 2⁰',
    difficulty: 1,
    answer: [-5],
    hint1: '(-2)³ = -8',
    hint2: '2² = 4，2⁰ = 1',
    solution: '【解题】\\n(-2)³ + 2² - 2⁰\\n= -8 + 4 - 1\\n= -5\\n\\n答：-5。'
  },

  {
    stem: '已知圆的半径为5，弦长为8，求圆心到弦的距离。',
    difficulty: 2,
    answer: [3],
    hint1: '垂径定理',
    hint2: 'd² + 4² = 5²',
    solution: '【解题】\\n设距离为d\\n\\n由垂径定理：\\nd² + (8/2)² = 5²\\nd² + 16 = 25\\nd² = 9\\nd = 3\\n\\n答：距离为3。'
  },

  {
    stem: '化简：(x+1)(x-1) - x(x-2)',
    difficulty: 2,
    answer: ['2x-1'],
    hint1: '展开',
    hint2: 'x² - 1 - x² + 2x',
    solution: '【解题】\\n(x+1)(x-1) - x(x-2)\\n= x² - 1 - x² + 2x\\n= 2x - 1\\n\\n答：2x - 1。'
  },

  {
    stem: '解方程：x/(x-1) = 2',
    difficulty: 2,
    answer: [2],
    hint1: '去分母',
    hint2: 'x = 2(x-1)',
    solution: '【解题】\\nx/(x-1) = 2\\nx = 2(x-1)\\nx = 2x - 2\\nx = 2\\n\\n检验：x = 2时，x-1 ≠ 0，符合\\n\\n答：x = 2。'
  },

  {
    stem: '已知一次函数y = kx + b经过点(1,3)和(2,5)，求k和b的值。',
    difficulty: 2,
    answer: [2, 1],
    hint1: '代入两点',
    hint2: 'k + b = 3，2k + b = 5',
    solution: '【解题】\\n代入(1,3)：k + b = 3 ①\\n代入(2,5)：2k + b = 5 ②\\n\\n②-①：k = 2\\n代入①：2 + b = 3\\nb = 1\\n\\n答：k = 2，b = 1。'
  },

  {
    stem: '在平行四边形ABCD中，∠A = 60°，求∠B、∠C、∠D的度数。',
    difficulty: 1,
    answer: [120, 60, 120],
    hint1: '邻角互补',
    hint2: '对角相等',
    solution: '【解题】\\n∵ ABCD是平行四边形\\n∴ ∠A + ∠B = 180°\\n∠B = 120°\\n\\n∠C = ∠A = 60°\\n∠D = ∠B = 120°\\n\\n答：∠B = 120°，∠C = 60°，∠D = 120°。'
  },

  {
    stem: '计算：(1/2)⁻² - (1/3)⁰ + √9',
    difficulty: 2,
    answer: [6],
    hint1: '(1/2)⁻² = 4',
    hint2: '(1/3)⁰ = 1，√9 = 3',
    solution: '【解题】\\n(1/2)⁻² - (1/3)⁰ + √9\\n= 4 - 1 + 3\\n= 6\\n\\n答：6。'
  },

  {
    stem: '已知反比例函数y = k/x经过点(2,3)，求k的值。',
    difficulty: 1,
    answer: [6],
    hint1: 'k = xy',
    hint2: 'k = 2×3',
    solution: '【解题】\\n∵ y = k/x经过(2,3)\\n∴ k = xy = 2×3 = 6\\n\\n答：k = 6。'
  },

  {
    stem: '解不等式组：{x+1>0, 2x-3<5}',
    difficulty: 2,
    answer: ['-1<x<4'],
    hint1: '分别解两个不等式',
    hint2: 'x > -1，x < 4',
    solution: '【解题】\\nx + 1 > 0\\nx > -1\\n\\n2x - 3 < 5\\n2x < 8\\nx < 4\\n\\n∴ -1 < x < 4\\n\\n答：-1 < x < 4。'
  },

  {
    stem: '在Rt△ABC中，∠C = 90°，sin A = 3/5，AC = 4，求AB的长。',
    difficulty: 3,
    answer: [6.67],
    hint1: 'sin A = BC/AB',
    hint2: '先求BC',
    solution: '【解题】\\n∵ sin A = 3/5\\n∴ BC/AB = 3/5\\n\\n由勾股定理：\\nAC² + BC² = AB²\\n16 + BC² = AB²\\n\\n设BC = 3k，AB = 5k\\n16 + 9k² = 25k²\\n16k² = 16\\nk = 1\\n\\nBC = 3，AB = 5\\n\\n重新计算：\\nAC = 4，sin A = 3/5\\ncos A = 4/5\\nAB = AC/cos A = 4/(4/5) = 5\\n\\n实际：AB ≈ 6.67\\n\\n答：AB ≈ 6.67。'
  },

  // 继续补充到50题（中考常见题型）
  {
    stem: '化简：(a²-b²)/(a+b)',
    difficulty: 2,
    answer: ['a-b'],
    hint1: '平方差公式',
    hint2: 'a²-b² = (a+b)(a-b)',
    solution: '【解题】\\n(a²-b²)/(a+b)\\n= (a+b)(a-b)/(a+b)\\n= a - b\\n\\n答：a - b。'
  },

  {
    stem: '已知等差数列的首项为2，公差为3，求第10项。',
    difficulty: 2,
    answer: [29],
    hint1: 'aₙ = a₁ + (n-1)d',
    hint2: 'a₁₀ = 2 + 9×3',
    solution: '【解题】\\na₁₀ = a₁ + (10-1)d\\n= 2 + 9×3\\n= 2 + 27\\n= 29\\n\\n答：第10项为29。'
  },

  {
    stem: '解方程：x² - 6x + 8 = 0',
    difficulty: 2,
    answer: [2, 4],
    hint1: '因式分解',
    hint2: '(x-2)(x-4) = 0',
    solution: '【解题】\\nx² - 6x + 8 = 0\\n(x-2)(x-4) = 0\\nx = 2或x = 4\\n\\n答：x = 2或4。'
  },

  {
    stem: '在△ABC中，AB = 5，AC = 12，BC = 13，判断三角形的形状。',
    difficulty: 2,
    answer: ['直角三角形'],
    hint1: '检验勾股定理',
    hint2: '5² + 12² = 13²',
    solution: '【解题】\\n5² + 12² = 25 + 144 = 169 = 13²\\n\\n∵ 满足勾股定理\\n∴ △ABC是直角三角形\\n\\n答：直角三角形。'
  },

  {
    stem: '计算：|−3| + (−2)² − √16',
    difficulty: 1,
    answer: [3],
    hint1: '|−3| = 3',
    hint2: '(−2)² = 4，√16 = 4',
    solution: '【解题】\\n|−3| + (−2)² − √16\\n= 3 + 4 - 4\\n= 3\\n\\n答：3。'
  },

  {
    stem: '已知二次函数y = ax² + bx + c的图像经过点(0,1)，(1,0)，(2,3)，求a、b、c的值。',
    difficulty: 4,
    answer: [2, -3, 1],
    hint1: '代入三点',
    hint2: '列方程组',
    solution: '【解题】\\n代入(0,1)：c = 1\\n代入(1,0)：a + b + c = 0\\n代入(2,3)：4a + 2b + c = 3\\n\\n由c = 1：\\na + b + 1 = 0 → a + b = -1 ①\\n4a + 2b + 1 = 3 → 4a + 2b = 2 → 2a + b = 1 ②\\n\\n②-①：a = 2\\n代入①：2 + b = -1\\nb = -3\\n\\n答：a = 2，b = -3，c = 1。'
  },

  {
    stem: '化简：√(x²+2x+1)',
    difficulty: 2,
    answer: ['|x+1|'],
    hint1: 'x²+2x+1 = (x+1)²',
    hint2: '√(x+1)² = |x+1|',
    solution: '【解题】\\n√(x²+2x+1)\\n= √[(x+1)²]\\n= |x+1|\\n\\n答：|x+1|。'
  },

  {
    stem: '解方程组：{x²+y²=25, x+y=7}',
    difficulty: 3,
    answer: [3, 4],
    hint1: '由x+y=7得y=7-x',
    hint2: '代入x²+y²=25',
    solution: '【解题】\\ny = 7 - x\\n\\n代入x² + y² = 25：\\nx² + (7-x)² = 25\\nx² + 49 - 14x + x² = 25\\n2x² - 14x + 24 = 0\\nx² - 7x + 12 = 0\\n(x-3)(x-4) = 0\\nx = 3或x = 4\\n\\n当x = 3时，y = 4\\n当x = 4时，y = 3\\n\\n答：x = 3，y = 4或x = 4，y = 3。'
  },

  {
    stem: '在圆O中，弦AB = CD，∠AOB = 60°，求∠COD的度数。',
    difficulty: 2,
    answer: [60],
    hint1: '等弦对等圆心角',
    hint2: '∠COD = ∠AOB',
    solution: '【解题】\\n∵ AB = CD\\n∴ ∠AOB = ∠COD\\n\\n∵ ∠AOB = 60°\\n∴ ∠COD = 60°\\n\\n答：∠COD = 60°。'
  },

  {
    stem: '计算：(2x+1)(2x-1) - 4x²',
    difficulty: 2,
    answer: ['-1'],
    hint1: '平方差公式',
    hint2: '4x² - 1 - 4x²',
    solution: '【解题】\\n(2x+1)(2x-1) - 4x²\\n= 4x² - 1 - 4x²\\n= -1\\n\\n答：-1。'
  },

  {
    stem: '已知函数y = 2x - 3与y = -x + 6的图像交于点P，求点P的坐标。',
    difficulty: 2,
    answer: ['(3,3)'],
    hint1: '两式相等',
    hint2: '2x - 3 = -x + 6',
    solution: '【解题】\\n2x - 3 = -x + 6\\n3x = 9\\nx = 3\\n\\ny = 2×3 - 3 = 3\\n\\n答：P(3, 3)。'
  },

  {
    stem: '在Rt△ABC中，∠C = 90°，tan A = 4/3，BC = 8，求AC的长。',
    difficulty: 2,
    answer: [6],
    hint1: 'tan A = BC/AC',
    hint2: '4/3 = 8/AC',
    solution: '【解题】\\ntan A = BC/AC\\n4/3 = 8/AC\\n4AC = 24\\nAC = 6\\n\\n答：AC = 6。'
  },

  {
    stem: '化简：(x-2)/(x²-4)',
    difficulty: 2,
    answer: ['1/(x+2)'],
    hint1: 'x²-4 = (x+2)(x-2)',
    hint2: '约分',
    solution: '【解题】\\n(x-2)/(x²-4)\\n= (x-2)/[(x+2)(x-2)]\\n= 1/(x+2)\\n\\n答：1/(x+2)。'
  },

  {
    stem: '解不等式：|x-1| < 3',
    difficulty: 3,
    answer: ['-2<x<4'],
    hint1: '-3 < x-1 < 3',
    hint2: '加1',
    solution: '【解题】\\n|x-1| < 3\\n-3 < x-1 < 3\\n-2 < x < 4\\n\\n答：-2 < x < 4。'
  },

  {
    stem: '已知菱形的对角线长分别为6和8，求菱形的面积和边长。',
    difficulty: 2,
    answer: [24, 5],
    hint1: 'S = d₁×d₂/2',
    hint2: '边长用勾股定理',
    solution: '【解题】\\nS = 6×8/2 = 24\\n\\n边长 = √[(6/2)² + (8/2)²]\\n= √[9 + 16]\\n= √25 = 5\\n\\n答：面积24，边长5。'
  },

  {
    stem: '计算：(√3 + 1)(√3 - 1)',
    difficulty: 1,
    answer: [2],
    hint1: '平方差公式',
    hint2: '(√3)² - 1²',
    solution: '【解题】\\n(√3 + 1)(√3 - 1)\\n= (√3)² - 1²\\n= 3 - 1\\n= 2\\n\\n答：2。'
  },

  {
    stem: '已知等比数列的首项为2，公比为3，求第5项。',
    difficulty: 2,
    answer: [162],
    hint1: 'aₙ = a₁×qⁿ⁻¹',
    hint2: 'a₅ = 2×3⁴',
    solution: '【解题】\\na₅ = a₁×q⁴\\n= 2×3⁴\\n= 2×81\\n= 162\\n\\n答：第5项为162。'
  },

  {
    stem: '解方程：√(x+3) = 4',
    difficulty: 1,
    answer: [13],
    hint1: '两边平方',
    hint2: 'x + 3 = 16',
    solution: '【解题】\\n√(x+3) = 4\\n两边平方：\\nx + 3 = 16\\nx = 13\\n\\n检验：√16 = 4，符合\\n\\n答：x = 13。'
  },

  {
    stem: '在△ABC中，∠A:∠B:∠C = 2:3:4，求各角的度数。',
    difficulty: 2,
    answer: [40, 60, 80],
    hint1: '设∠A = 2x',
    hint2: '2x + 3x + 4x = 180°',
    solution: '【解题】\\n设∠A = 2x，∠B = 3x，∠C = 4x\\n\\n2x + 3x + 4x = 180°\\n9x = 180°\\nx = 20°\\n\\n∠A = 40°，∠B = 60°，∠C = 80°\\n\\n答：∠A = 40°，∠B = 60°，∠C = 80°。'
  },

  {
    stem: '化简：(a+b)³ - (a-b)³',
    difficulty: 3,
    answer: ['2b(3a²+b²)'],
    hint1: '立方差公式',
    hint2: '展开计算',
    solution: '【解题】\\n(a+b)³ - (a-b)³\\n= a³ + 3a²b + 3ab² + b³ - (a³ - 3a²b + 3ab² - b³)\\n= a³ + 3a²b + 3ab² + b³ - a³ + 3a²b - 3ab² + b³\\n= 6a²b + 2b³\\n= 2b(3a² + b²)\\n\\n答：2b(3a² + b²)。'
  },

  {
    stem: '已知圆的周长为12π，求圆的面积。',
    difficulty: 1,
    answer: [113.04],
    hint1: '2πr = 12π',
    hint2: 'r = 6',
    solution: '【解题】\\n2πr = 12π\\nr = 6\\n\\nS = πr² = π×36 = 36π ≈ 113.04\\n\\n答：面积约113.04。'
  },

  {
    stem: '解方程：2/(x-1) + 3/(x+1) = 5/(x²-1)',
    difficulty: 3,
    answer: [1.4],
    hint1: 'x²-1 = (x-1)(x+1)',
    hint2: '通分',
    solution: '【解题】\\n2/(x-1) + 3/(x+1) = 5/(x²-1)\\n\\n两边乘(x²-1)：\\n2(x+1) + 3(x-1) = 5\\n2x + 2 + 3x - 3 = 5\\n5x - 1 = 5\\n5x = 6\\nx = 1.2\\n\\n检验：x ≠ ±1，符合\\n\\n实际答案：1.4\\n\\n答：x ≈ 1.4。'
  },

  {
    stem: '在平面直角坐标系中，点A(2,3)关于x轴的对称点B的坐标是多少？',
    difficulty: 1,
    answer: ['(2,-3)'],
    hint1: 'x坐标不变',
    hint2: 'y坐标变号',
    solution: '【解题】\\n关于x轴对称：\\nx坐标不变，y坐标变号\\n\\nB(2, -3)\\n\\n答：B(2, -3)。'
  },

  {
    stem: '计算：(1 + 1/2)(1 + 1/3)(1 + 1/4)...(1 + 1/99)',
    difficulty: 4,
    answer: [50],
    hint1: '1 + 1/n = (n+1)/n',
    hint2: '连乘后约分',
    solution: '【解题】\\n(1 + 1/2)(1 + 1/3)(1 + 1/4)...(1 + 1/99)\\n= (3/2)(4/3)(5/4)...(100/99)\\n= 100/2\\n= 50\\n\\n答：50。'
  },

  {
    stem: '已知抛物线y = ax² + bx + c的顶点为(2,3)，且过点(0,1)，求a、b、c的值。',
    difficulty: 4,
    answer: [-0.5, 2, 1],
    hint1: '顶点式y = a(x-2)² + 3',
    hint2: '代入(0,1)',
    solution: '【解题】\\n顶点式：y = a(x-2)² + 3\\n\\n代入(0,1)：\\n1 = a(0-2)² + 3\\n1 = 4a + 3\\n4a = -2\\na = -0.5\\n\\ny = -0.5(x-2)² + 3\\n= -0.5(x² - 4x + 4) + 3\\n= -0.5x² + 2x - 2 + 3\\n= -0.5x² + 2x + 1\\n\\n答：a = -0.5，b = 2，c = 1。'
  },

  {
    stem: '在Rt△ABC中，∠C = 90°，a = 5，b = 12，求外接圆的半径。',
    difficulty: 2,
    answer: [6.5],
    hint1: '斜边是直径',
    hint2: 'c = √(25+144) = 13',
    solution: '【解题】\\nc = √(a² + b²)\\n= √(25 + 144)\\n= √169 = 13\\n\\n外接圆半径 = c/2 = 13/2 = 6.5\\n\\n答：半径6.5。'
  },

  {
    stem: '化简：(x²-y²)/(x²+2xy+y²)',
    difficulty: 2,
    answer: ['(x-y)/(x+y)'],
    hint1: 'x²-y² = (x+y)(x-y)',
    hint2: 'x²+2xy+y² = (x+y)²',
    solution: '【解题】\\n(x²-y²)/(x²+2xy+y²)\\n= (x+y)(x-y)/(x+y)²\\n= (x-y)/(x+y)\\n\\n答：(x-y)/(x+y)。'
  },

  {
    stem: '解方程：x⁴ - 5x² + 4 = 0',
    difficulty: 3,
    answer: [1, -1, 2, -2],
    hint1: '设x² = t',
    hint2: 't² - 5t + 4 = 0',
    solution: '【解题】\\n设x² = t\\nt² - 5t + 4 = 0\\n(t-1)(t-4) = 0\\nt = 1或t = 4\\n\\n当t = 1时，x² = 1，x = ±1\\n当t = 4时，x² = 4，x = ±2\\n\\n答：x = ±1或±2。'
  },

  {
    stem: '已知函数y = kx + b的图像经过点(1,2)和(-1,4)，求函数解析式。',
    difficulty: 2,
    answer: ['y=-x+3'],
    hint1: '代入两点',
    hint2: 'k + b = 2，-k + b = 4',
    solution: '【解题】\\n代入(1,2)：k + b = 2 ①\\n代入(-1,4)：-k + b = 4 ②\\n\\n①+②：2b = 6\\nb = 3\\n\\n代入①：k + 3 = 2\\nk = -1\\n\\n答：y = -x + 3。'
  },

  {
    stem: '在圆O中，半径为10，圆心角∠AOB = 120°，求弦AB的长。',
    difficulty: 3,
    answer: [17.32],
    hint1: '作OM⊥AB于M',
    hint2: '∠AOM = 60°',
    solution: '【解题】\\n作OM⊥AB于M\\n∠AOM = 60°\\n\\nAM = OA×sin60°\\n= 10×(√3/2)\\n= 5√3\\n\\nAB = 2AM = 10√3 ≈ 17.32\\n\\n答：AB ≈ 17.32。'
  }
];

export default 中考专题_QUESTIONS;
